A real estate agency collects the data in the following table concerning y = sales price of a house (in thousands of dollars) x1 = home size (in hundreds of square feet) x2 = rating (an overall "niceness rating" for the house expressed on a scale from 1 [worst] to 10 [best], and provided by the real estate agency) Sales Price, y (x $1000) 180 98.1 173.1 136.5 141 165.9 193.5 127.8 163.5 172.5 Home Size, x₁ (x 100 ft²) Modell: y Bo + B₁x₁ + B₂x2₂ +€ Model2: y = Bo + B₁x₁ + B₂x₂ + B3x² + € 23 11 20 17 15 21 24 13 19 25 Make a comparison between models: (f) Based on their Råbj Rating, X₂ 46967 ∞0 WON st 2 9 3 8 The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. 2 Use software of your choice to fit the 2 following models. Then answer the same questions (a-e) for both models. (a) Discuss why scatter plot of y vs x₁ and x₂ indicate that this model might be reasonable. (b) Interpret the regression coefficients (c) Test significance of each individual coefficients. (d) Test overall regression model (e) For an individual house with size-2000 Square feet and rating-8 find point estimation, 95% C.I. and 95% P.I.
A real estate agency collects the data in the following table concerning y = sales price of a house (in thousands of dollars) x1 = home size (in hundreds of square feet) x2 = rating (an overall "niceness rating" for the house expressed on a scale from 1 [worst] to 10 [best], and provided by the real estate agency) Sales Price, y (x $1000) 180 98.1 173.1 136.5 141 165.9 193.5 127.8 163.5 172.5 Home Size, x₁ (x 100 ft²) Modell: y Bo + B₁x₁ + B₂x2₂ +€ Model2: y = Bo + B₁x₁ + B₂x₂ + B3x² + € 23 11 20 17 15 21 24 13 19 25 Make a comparison between models: (f) Based on their Råbj Rating, X₂ 46967 ∞0 WON st 2 9 3 8 The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. 2 Use software of your choice to fit the 2 following models. Then answer the same questions (a-e) for both models. (a) Discuss why scatter plot of y vs x₁ and x₂ indicate that this model might be reasonable. (b) Interpret the regression coefficients (c) Test significance of each individual coefficients. (d) Test overall regression model (e) For an individual house with size-2000 Square feet and rating-8 find point estimation, 95% C.I. and 95% P.I.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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solve d,e,f please
![A real estate agency collects the data in the following table concerning:
- **y** = sales price of a house (in thousands of dollars)
- **x₁** = home size (in hundreds of square feet)
- **x₂** = rating (an overall "niceness rating" for the house expressed on a scale from 1 [worst] to 10 [best], provided by the real estate agency)
| Sales Price, y ($1000) | Home Size, x₁ (× 100 ft²) | Rating, x₂ |
|------------------------|--------------------------|------------|
| 180 | 23 | 5 |
| 98.1 | 11 | 2 |
| 173.1 | 20 | 9 |
| 136.5 | 17 | 3 |
| 141 | 15 | 8 |
| 165.9 | 21 | 9 |
| 193.5 | 24 | 7 |
| 127.8 | 13 | 6 |
| 163.5 | 19 | 7 |
| 172.5 | 25 | 2 |
The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. Use software of your choice to fit the 2 following models. Then answer the same questions (a-e) for both models.
Model1: \[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \epsilon \]
Model2: \[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_2^2 + \epsilon \]
Questions:
(a) Discuss why scatter plot of y vs x₁ and x₂ indicate that this model might be reasonable.
(b) Interpret the regression coefficients.
(c) Test significance of each individual coefficients.
(d) Test overall regression model.
(e) For an individual house with size = 2000 Square feet and rating = 8, find point estimation, 95% C.I. and 95% P.I.
Make a comparison between models:
(f) Based on their \( R^2_{adj} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9e27b5d-0ab8-428e-954d-97d64fc14c61%2F1528689d-a4d0-4b32-ae20-6ced88fba3b9%2F0h0hw3k_processed.png&w=3840&q=75)
Transcribed Image Text:A real estate agency collects the data in the following table concerning:
- **y** = sales price of a house (in thousands of dollars)
- **x₁** = home size (in hundreds of square feet)
- **x₂** = rating (an overall "niceness rating" for the house expressed on a scale from 1 [worst] to 10 [best], provided by the real estate agency)
| Sales Price, y ($1000) | Home Size, x₁ (× 100 ft²) | Rating, x₂ |
|------------------------|--------------------------|------------|
| 180 | 23 | 5 |
| 98.1 | 11 | 2 |
| 173.1 | 20 | 9 |
| 136.5 | 17 | 3 |
| 141 | 15 | 8 |
| 165.9 | 21 | 9 |
| 193.5 | 24 | 7 |
| 127.8 | 13 | 6 |
| 163.5 | 19 | 7 |
| 172.5 | 25 | 2 |
The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. Use software of your choice to fit the 2 following models. Then answer the same questions (a-e) for both models.
Model1: \[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \epsilon \]
Model2: \[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_2^2 + \epsilon \]
Questions:
(a) Discuss why scatter plot of y vs x₁ and x₂ indicate that this model might be reasonable.
(b) Interpret the regression coefficients.
(c) Test significance of each individual coefficients.
(d) Test overall regression model.
(e) For an individual house with size = 2000 Square feet and rating = 8, find point estimation, 95% C.I. and 95% P.I.
Make a comparison between models:
(f) Based on their \( R^2_{adj} \).
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